Physical Quantities:

In physical science, we commonly deal with quantities such as pressure, volume, mass, temperature, current, etc. These quantities are known as physical quantities.

A physical quantity has two components, namely, numerical value and its unit and is written as,
Physical quantity  Numerical value  unit 

Here Physical quantity Newton and its numerical value 5
C.G.S Units 
S.I Units 
Physical quantity  Dimension 
Length  L 
Mass  M 
Time  T 
Definition of Base Physical Quantities:
Metre:

The metre is the length of path traveled by light in vacuum during a time interval 1/299 792 458 of a second.
 Unit and dimension of Area:

Area = Length × Length
Thus the unit of Area = Unit of Length × Unit of Length

Unit of Area in C.G.S. System = cm × cm
= cm²

Unit of Area in S.I. System is = m × m
= m²

Dimension of Area = L × L
= [L]²
 Unit and dimension of Volume:

Volume (V) = Length × Length × Length.
Thus the unit of Volume = Length × Length × Length.

Unit of Area in C.G.S. System = cm × cm × cm
= cm³

Unit of Area in S.I. System is = m × m × m
= m³

Dimension of Area = L × L × L
= [L³]
 Unit and dimension of Density:

From the definition of Density (d) = Mass/Volume
Thus the unit of density = Unit of Mass/Unit of Volume.

Unit of Area in C.G.S. System = gm/cm³
= gm cm⁻³

Unit of Area in S.I. System is = Kg/m³
= Kg m⁻³

Dimension of Area = [M]/[L³]
= [M L⁻³]
 Unit and dimension of Force:

From the Newton Second Low of Motion,
Force = Mass × Acceleration
or, Force = Mass × Velocity/Time
or, Force = Mass × (Length/Time) /Time

Here Velocity = Length/Time

∴ Force = Mass × (Length/Time²)

Thus the unit of Force in C.G.S. System,
=Unit of Mass × (Unit of Length/Unit of Time²)

= gm × cm/sec²
= gm cm/sec²
or, gm cm sec⁻²
or, Dyne

Again in the same way Unit of Force in S.I System,
= Kg m/sec²
or, Kg m sec⁻²
or, Newton

From the above discussion dimension of Force, = dimension of Mass × dimension of Length/dimension of Time².

Thus the dimension of Force = [M L T⁻²]

Convert 1 newton into dyne:

1 Newton = Kg m/sec²
= (1 Kg× 1 m )/(1 sec)²

We know that, 1 Kg = 10³ gm and 1 m = 10² cm

Thus, 1 Newton = (10³gm × 10² cm)/(1 sec)²
= 10⁵ gm cm/sec2
= 10⁵ Dyne
 Unit and dimension of Work:

From the definition of Work (W) = Force(F) × Displacement(d).
Thus, the unit Work = unit of Force × unit of Displacement(d)

∴ Unit of Work in C.G.S. System, = (gm cm/sec²) × cm
or, gm cm²/sec²
or, gm cm²sec⁻²
or, erg

And unit of work in S.I. system = (Kg m/sec²) × m
or, Kg m²/sec²
or, Kg m²sec⁻²
or, Joule

From the above discussion dimension of Work, = (dimension of Mass × dimension of Length)²)/(dimension of Time²)

Thus dimension of Work = [ML²T⁻²]

Convert 1 Joule into erg:

1 Joule = 1 Kg m²/sec²
= (1 Kg × 1 m² )/1 sec²

We know that, 1 Kg = 10³ gm and 1 m = 10² cm

Thus, 1 Joule = {10³ gm × (10²)² cm}/1 sec²
= 10⁷ gram cm²/sec²

= 10⁷ erg
 Unit and dimension of Force:

The ability to doing work is termed as Energy. Thus, the unit and dimension of energy and work is same.

Unit of Energy in C.G.S System is erg
and S.I. System is Joule
 Unit and dimension of Pressure:

From the definition of Pressure (P) = Force/Area
Thus the unit of Pressure = Unit of force/Unit of area.

Unit of Pressure in C.G.S. System = erg/cm²
= erg cm⁻²

Unit of Pressure in S.I. System is = joule/m²
= joule m⁻²

Dimension of Pressure = [M L⁻²]